Define a Set $S$ Recursively as Follows:
I $11 \in S$ II RECURSION:
A

question 31

Essay

Define a set $S$ recursively as follows:
I. BASIS: $11 \in S$
II. RECURSION:
a. If $s \in S$ , then $0 s \in S$ and $s 0 \in S$
b. If $x$ is any string (including the null string) such that $1 x 1 \in S$ , then $10 x 1 \in S$ and $1 x 01 \in S$ III. RESTRICTION: No strings other than those derived from I and II are in $S$ .
a. Is $010010 \in S$ ? Justify your answer.
b. Is $011011 \in S$ ? Justify your answer.

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